Mosco convergence of Dirichlet forms in infinite dimensions with changing reference measures

摘要

Let E be an infinite-dimensional locally convex space, let {mu(n)} be a weakly convergent sequence of probability measures on E, and let {E-n} be a sequence of Dirichlet forms on E such that E-n is defined on L-2(mu(n)). General sufficient conditions for Mosco convergence of the gradient Dirichlet forms are obtained. Applications to Gibbs states on a lattice and to the Gaussian case are given. Weak convergence of the associated processes is discussed. (C) 2005 Elsevier Inc. All rights reserved.